My brother and I arrived at a show in NYC during the Vertigo tour very early in the morning. So early we were the first there. I guess you can say we ended up being the 'line mods' without asking or wanting the job. We tried to pass it off to the people who started showing up but no one wanted the job. So the answer to your question is no, it's whoever shows up first that ends up trying to keep the line in order.
We were the first to enter the venue from the the GA line. There were quite a few people already in including all of the disabled fans. I assumed there was a different entrance for them because no one passed us on the way in.